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Crack Closure and Stress Intensity Factor Measurements in Nodular Crack closure and stress intensity factor measurements in nodular graphite cast iron using three-dimensional correlation of laboratory X-ray microtomography images Nathalie Limodin, Julien Réthoré, Jean-Yves Buffiere, Anthony Gravouil, François Hild, Stéphane Roux To cite this version: Nathalie Limodin, Julien Réthoré, Jean-Yves Buffiere, Anthony Gravouil, François Hild, et al.. Crack closure and stress intensity factor measurements in nodular graphite cast iron using three-dimensional correlation of laboratory X-ray microtomography images. Acta Materialia, Elsevier, 2009, 57, pp.4090- 4101. hal-00410325 HAL Id: hal-00410325 https://hal.archives-ouvertes.fr/hal-00410325 Submitted on 19 Aug 2009 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Text only Crack closure and stress intensity factor measurements in nodular graphite cast iron using 3D correlation of laboratory X-ray microtomography images Nathalie Limodina, Julien Réthoréb, Jean-Yves Buffièrea, Anthony Gravouilb, François Hildc, Stéphane Rouxc. (a) MATEriaux Ingénierie et Sciences (MATEIS), INSA-Lyon / CNRS-UMR 5510, Bât. Saint Exupéry, 20 avenue Albert Einstein, F-69621 Villeurbanne Cedex, France (b) Laboratoire de Mécanique des Contacts et des Structures (LaMCoS), INSA-Lyon / CNRS-UMR 5259, 20 avenue Albert Einstein, F-69621 Villeurbanne Cedex, France (c) Laboratoire de Mécanique et Technologie (LMT-Cachan), ENS Cachan / CNRS / UPMC / PRES UniverSud Paris, 61 avenue du Président Wilson, F-94235 Cachan Cedex, France Abstract : 3D tomographic images of a nodular graphite cast iron obtained using a laboratory X-ray source were used to analyze the opening of a fatigue crack during in-situ mechanical loading. Direct image analysis and digital image correlation are utilized to obtain the 3D morphology and front location of the crack as well as the displacement fields in the bulk of the specimen. From DIC results, it is possible to extract the Crack Opening Displacement (COD) map in the whole sample cross-section and to compute Stress Intensity Factors (SIF) all along the crack front even for COD values that are less than the image resolution. The comparison of COD maps with local values of SIF enabled for an estimation of the opening SIF, Kop, equal to 6 MPa√m. Keywords: X-ray microtomography, 3D Digital Image Correlation, Stress Intensity Factors, Nodular graphite cast iron. 1 Introduction Fatigue crack closure was first described by Elber [1] more than 30 years ago. Although it is a critical issue for life time predictions through Paris’ laws (with the use of effective stress 1 Linking powered by eXtyles intensity factor ranges, ΔKeff), there is still no unified method of measurement that reaches general consensus. Crack closure occurs when the crack surfaces come into contact before the minimum load of the fatigue cycle is reached. The underlying mechanisms are diverse and may operate simultaneously; the reader is referred to ref. [2] for a more complete description. For example, a growing crack leaves behind a plastically deformed zone that is adjacent to the crack faces. This plastic wake induces early closure of the crack during unloading via a mechanism called Plasticity-Induced Crack Closure (PICC). Furthermore, asperities on the crack faces may also result in premature contact and induce Roughness- Induced Crack Closure (RICC). This mechanism becomes significant near the fatigue threshold when crack paths are highly crystallographic or under mode II or III loading that favours asperity contacts; in this case, closure concentrates in regions where the crack changed its direction of propagation [3]. Therefore, ideally, to measure crack closure and identify the operative closure mechanism, one needs a way to measure precisely the crack mouth displacements or contact along the crack front knowing the topography of the crack. Measurements at the surface of a sample during a loading/unloading cycle have been performed using for example scanning electron microscopy [4]. Surface measurements allow one to visualize crack shapes and to analyze closure changes with the crack length [5]. However the relevance of this kind of measurement with respect to the bulk of the sample can be questioned. Bulk measurements of crack closure involve indirect observations from crack growth, e.g. with potential drop or acoustic emission, and with mechanical compliance curves [6]. This last method is the most widely used. The loss of linearity of the displacement-load curve recorded during unloading of the specimen delimits the closure load. However, the result may depend on the positioning of the displacement gauge, namely, at the crack mouth, at the back face of the specimen, behind the crack tip within the specimen (push-rod gauge) or near the crack tip at the surface [6]. With these techniques, no information on the relationship between crack topography and closure can be obtained as the detailed crack shape is not available. 2 Linking powered by eXtyles Three-dimensional visualisation of cracks in optically opaque materials such as metals is now possible using high resolution X-ray tomography [7-13]. So far, synchrotron X-rays have been used for this kind of studies as crack detection is enhanced by the high spatial coherence of X-ray beams available at modern (third generation) synchrotron facilities [14]. However, the use of synchrotron radiation puts a strong limit on the number of experiments that can be carried out in situ. 3D tomography images can be used, in principle, to evaluate the 3D displacement field at the crack tip in a specimen under load. In practice, this can be achieved using two different methods, namely Particle Tracking (PT) and Digital Image Correlation (DIC). Particle Tracking consists in measuring the displacements of microstructural features or markers inside the material. These markers are first identified by their gravity centre. Then, they are individually tracked between 3D images of the same specimen under different loads in order to compute the global displacement field inside the specimen. The DIC method is well established for computing displacements and strains on the surface of samples or structures [15-17]. It consists in measuring displacement fields between image pairs of the same specimen at different loads. The displacement field is obtained, using the so-called brightness conservation, so that the image of the loaded sample is matched to the reference image when pixel locations are corrected for by the measured displacement field. Recent developments have made possible the extension of this Galerkin technique to 3D displacement measurements in the bulk of specimens using 3D tomography images [18]. The uncertainty level of the latter is usually smaller than that of the former. Both techniques have been applied to very different materials (Table 1). For example, the architecture in a trabecular bone [19] or in an open-cell aluminium foam [20] has been proved a valid texture for 3D DIC while microporosity in an aluminium alloy has been successfully used for particle tracking [21; 22]. The resolution of both techniques depends directly on the presence of numerous and finely dispersed microstructural features inside the material and those features should not break nor deform heavily upon loading. If the material 3 Linking powered by eXtyles does not possess a natural texture that meets these requirements, artificial markers may be added. For example, tungsten particles were added to an aluminium matrix [23; 24] and microholes were laser-drilled in a dispersion-strengthened copper alloy [25] to allow for strain mapping in tensile testing for strain values ranging from 3 [23; 25] to 22% [25]. However, the influence of artificial markers on the matrix behaviour is difficult to assess. Increasing the number of artificial markers enhances the spatial resolution of strain mapping via tracking methods but it may also reinforce their potential perturbation effect. Whenever possible, the use of a material that possesses a natural texture suitable for DIC/PT is thus preferable. Measurement of crack closure has been carried out by manual tracking of microstructural features using high resolution synchrotron radiation (0.7 µm voxel size). It drew interesting results on the relationship between the crack shape and local values of the stress intensity factor [21]. However, this technique has the disadvantage that crack tip displacements are not measured automatically. This paper is a first attempt to evaluate crack closure in a widely used structural material, i.e. a nodular graphite cast iron where the graphite nodules act as natural markers to determine 3D displacements and stress intensity factors by correlating images obtained with standard laboratory X-ray tomography equipment. 2 Material and experimental methods 2.1 Material The material of this study is a ferritic cast iron whose composition is 3.4 wt% C, 2.6 wt% Si, 0.05 wt% Mg, 0.19 wt% Mn, 0.005 wt% S, and 0.01 wt% P. After casting and heat treatment (ferritization at 880 °C followed by air cooling) the microstructure obtained is a ferritic matrix (98 wt% ferrite and 2 wt% perlite; average grain size 50 µm) with a 14 % volume fraction of graphite nodules. Carbon (nodules) and iron (matrix) have atomic numbers that are different enough to give a strong X-ray attenuation contrast. Therefore, the spherical nodules, which 4 Linking powered by eXtyles are homogeneously distributed inside the matrix, are easily imaged by tomography and they can be used as natural markers for image correlation in the 3D reconstructed images. The average nodule diameter of 45 µm is large enough to allow for a relatively low resolution voxel size to be used for tomography.
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